Chapter 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications
Abstract The purpose of this chapter is to discuss the investment and financing policy is discussed; the role of interaction between investment, financing, and dividends the financing mix in analyzing investment opportunities will policy of the firm. A brief introduction of the policy receive detailed treatment. Again, the recognition of risky framework of finance is provided in Sect. 2.1. Section 2.2 dis- debt will be allowed, so as to lend further practicality to the cusses the interaction between investment and dividends pol- analysis. The recognition of financing and investment effects icy. Section 2.3 discusses the interaction between dividends are covered in Sect. 2.5, where capital-budgeting techniques and financing policy. Section 2.4 discusses the interaction be- are reviewed and analyzed with regard to their treatment of tween investment and financing policy. Section 2.5 discusses the financing mix. In this section several numerical compar- the implications of financing and investment interactions for isons are offered, to emphasize that the differences in the capital budgeting. Section 2.6 discusses the implications of techniques are nontrivial. Section 2.6 will discuss implica- different policies on the beta coefficients. The conclusion is tion of different policies on systematic risk determination. presented in Sect. 2.7. Summary and concluding remarks are offered in Sect. 2.7.
Keywords Investment policy r Financing policy r Dividend policy r Capital structure r Financial analysis r Financial 2.2 Investment and Dividend Interactions: planning, Default risk of debt r Capital budgeting r System- The Internal Versus External Financing atic risk Decision
Internal financing consists primarily of retained earnings and depreciation expense, while external financing is comprised 2.1 Introduction of new equity and new debt, both long and short term. Deci- sions on the appropriate mix of these two sources for a firm This chapter discusses the three-way interaction between in- are likely to affect both the payout ratio and the capital struc- vestment, financing, and dividend decisions. As shown in fi- ture of the firm, and this in turn will generally affect its mar- nancial policy literature, there exists a set of ideal conditions ket value. In this section an overview of internal and external under which there will be no interaction effects between the financing is provided, with the discussion culminating in a areas of concern. However, the ideal conditions imposed by summary of the impacts that earnings retention or earnings academicians to analyze the effects dividend and financing payout (with or without supplemental financing from exter- policy have on the investment decision and the value of the nal sources) can have on a firm’s value and on planning and firm are not realistic, when one considers financial manage- forecasting. ment in the real world. Thus, an overview of the interactions of financing, investment, and dividend decisions is important for those concerned with financial analysis and planning. This chapter sequentially addresses the three interaction Internal Financing effects. In Sect. 2.2 the relation between investment and div- idend policy is explored through a discussion of internal vs. Changes in equity accounts between balance-sheet dates are external financing, with the emphasis on the use of retained generally reported in the statement of retained earnings. earnings as a substitute for new equity, or vice versa. The Retained earnings are most often the major internal source interaction between corporate financing and dividend poli- of funds made available for investment by a firm. The cost of cies will be covered in Sect. 2.3, where default risk on debt these retained earnings is generally less than the cost associ- is recognized. Then in Sect. 2.4, the interaction between ated with raising capital through new common-stock issues.
C.-F. Lee et al. (eds.), Handbook of Quantitative Finance and Risk Management, 23 DOI 10.1007/978-0-387-77117-5_2, c Springer Science+Business Media, LLC 2010 24 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications
Table 2.1 Payout ratio Ð 1962 0.58 1974 0.405 1986 0.343 1998 0.234 composite for 500 firms 1963 0:567 1975 0:462 1987 0:559 1999 0.435 1964 0:549 1976 0:409 1988 0:887 2000 0.299 1965 0:524 1977 0:429 1989 0:538 2001 0.383 1966 0:517 1978 0:411 1990 0:439 2002 0.04 1967 0:548 1979 0:38 1991 0:418 2003 0.259 1968 0:533 1980 0:416 1992 0:137 2004 0.311 1969 0:547 1981 0:435 1993 0:852 2005 0.282 1970 0:612 1982 0:422 1994 0:34 2006 0.301 1971 0:539 1983 0:399 1995 0:346 1972 0:491 1984 0:626 1996 0:327 1973 0:414 1985 0:525 1997 0:774
It follows that retained earnings, rather than new equity, financing will have different effects on the growth rate of should be used to finance further investment if equity is to be earnings per share, of dividends per share, and, presumably, used and the dividend policy (dividends paid from retained of the share price itself. earnings) is not seen to matter. The availability of retained Higgins (1977) considered the amount of growth a firm earnings is then determined by the firm’s profitability and could maintain if it was subject to an external equity con- the payout ratio, the latter being indicative of dividend pol- straint and sought to maintain certain debt and payout ratios. icy. Thus we find that the decision to raise funds externally He was able to show the sustainable growth rate in sales, S , may be dependent on dividend policy, which in turn may af- to be: fect investment decisions. p.1 d/.1 C L/ .rr/.ROE/ The payout ratios indicated in Table 2.1 show that, on av- S D D (2.1) erage, firms in the S&P 500 retained more than 50% of their t p.1 d/.1 C L/ 1 .rr/.ROE/ earnings after 1971 rather than pay them out in dividends. where p, profit margin on sales; d, dividend payout ratio; L, This is done because of the investment opportunities avail- debt-to-equity ratio; t, total asset-to-sales ratio; rr, retention able for a firm, and indicates that retained earnings are a ma- rate; ROE, return on equity. jor source of funds for a firm. Higgins (1977) used 1974 U.S. manufacturing firms’ composite financial statement data as an example to calculate S . Using the figures p D 5:5%;d D 33%;L D 88%and External Financing t D 73%, he obtained:
.0:055/.1 0:33/.1 C 0:88/ External financing usually takes one of two forms, debt S D D 10:5% 0:73 .0:055/.1 0:33/.1 C 0:88/ financing or equity financing. We leave the debt vs. equity question to subsequent sections, and here directly confront Using this method we can calculate sustainable growth rate only the decision whether to utilize retained earnings or new in sales for financial analysts and planning models. common stock to finance the firm. From this we can see that a firm with many valuable in- We have previously shown that the market value of the vestment opportunities may be forced to forego some of these firm is unaffected by such factors if dividend policy and cap- opportunities due to capital constraints, and the value of the ital structure are irrelevant. It should also be clear that div- firm will not be maximized as it could have been. Dividend idend policy and capital structure can affect market values. and capital-structure decisions relate directly to investment Therefore, the consideration of an optimal internal-external decisions. While it may not be reasonable to assume that the financing combination is important in the field of financial firm could not issue new equity, the question is at what cost management. This optimal combination is a function of the it can be raised under such a constraint. payout ratio, the debt-to-equity ratio, and the interaction be- In an even more practical vein, Higgins also incorpo- tween these two decision variables. From this it can be shown rated inflation into his model, acknowledging the fact that (and this will be the topic of discussion in the following para- most depreciation methods that serve to make depreciation a graphs) that different combinations of internal and external source of funds are founded on historical costs, and not the 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications 25 replacement values the firm must pay to sustain operations taining a high payout rate and financing further investment at their current level. Introducing the new variables defined with new-equity issues. below, it is possible to define sustainable growth in real and nominal terms, the former being the item of interest here. Let c, nominal current assets to nominal sales; f, nominal 2.3 Interactions Between Dividend fixed assets to real sales; j, inflation rate. and Financing Policies So real sustainable growth Sr is If we were able to hold the capital structure of firms con- .1 C j/p.1 d/.1 C L/ jc S D : stant, then we would be able to determine the advantage or r .1 C j/c C f .1 C j/p.1 d/.1 C L/ (2.2) disadvantage of internal financing relative to external financ- ing. Van Horne and McDonald, as briefly mentioned before, Using figures from the manufacturing sector and an inflation were able to empirically test for the effects created by ei- rate of 10%, which at the time of writing was approximately ther policy, providing the substance for a major part of the the actual inflation rate then prevailing, it was found that following discussion. If we were to go into more depth and real sustainable growth was only a third of that of the nom- specifically consider firms that issue risky debt while main- inal figure; this serves to further emphasize the importance taining shareholder’s limited-liability status, and still keep- of the interaction between dividend policy and investment ing to the chosen internal or external equity plan, then the decisions, since the former acts as a constraint on the lat- interactions between financing and investment decisions can ter. Higgins (1977) paper has recently been generalized by affect the relative positions of stock and bondholders. Black Johnson (1981)andHiggins (1981). (1976) argued that a possible strategy a firm could follow to The usual caveat associated with the dividend-irrelevance transfer economic resources from bondholders to stockhold- proposition is that investment policy is unaffected; that is, ers is to pay as generous dividends as possible. In this way new equity is issued to replace those retained earnings that the internal-external financing plan is predetermined, as pay- are paid out. Here we emphasize new equity with the in- ing large dividends jeopardizes the bondholders’ position as tent of avoiding financing-policy questions. Knowing that the assets are siphoned away from the firm, all to the gain of the flotation costs involved with new issues could be avoided shareholders. by employing retained earnings, the effect such a strategy In this section the interactions between dividend and fi- has on firm value is largely an empirical question. Any nancing policy will be analyzed in terms of (1) cost of equity such tests directed toward this issue must also recognize that capital and (2) the default-risk viewpoint of debt. there may be a preference for dividends that may dominate or mitigate the flotation-cost effects. With these factors in mind, Van Horne and McDonald (1971) ran cross-sectional regressions on samples of utility stocks and electronics man- Cost of Equity Capital and Dividend Policy1 ufacturers to see whether dividend payouts and the rates of new issues of common stocks had significant effects on price- Van Horne and McDonald (1971) chose to develop a earnings ratios. The utility industry results indicate that, at cross-sectional model to test for the significance of dividend the lower end of the new-equity issue spectrum, the dividend- payouts in the valuation process in the electric utility indus- preference effect overshadowed the flotation-cost effect, a try. The use of the electric utility industry proved to be op- result that appeared to shift in direction when higher levels erationally less difficult than other industries because it was of new equity financing were considered. Further analysis desired to hold interfirm differences constant, and indepen- into the dividend-preference question has been performed by dent variable selection to this end was relatively straight- Litzenberger and Ramaswamy (1979). Using a generalized forward. Since the authors were interested in capitalization capital-asset-pricing model, they examined this trade-off be- rates, year-end P/E ratios were selected to be the dependent tween dividend preference and tax effects, all in an effort to variables.1 This value was thought to be a function of three justify the contention of an optimal dividend policy. The re- variables: growth in assets, dividend payout, and financial sults presented by Van Horne and McDonald were admittedly risk. The latter variable is considered sufficient for this sam- tentative (especially since the electronics industry sample ple due to the homogeneity of the other aspects of the in- yielded few corroborating results), and most of the t-statistics cluded firm’s risks. The model can be written out and more associated with the utility sample new-issue coefficients were carefully defined by the following; quite low. The strongest statement that could be made follow- ing this analysis is that there appears to be little detrimental P=E D a C a g C a p C a R C u; (2.3) effect on firm valuation from following a strategy of main- 0 1 2 3 26 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications where g, compound growth of assets over eight previous ences). Empirical results are indicated in the lower portion years; p, dividend payout ratio on an annual basis; Lev, of Table 2.2. However, by replacing the dummy variable of interest charges/[operating revenues Ð operating expenses]; Group E for any one of the four dummy variables discussed u, error term. above, Van Horne and McDonald found that the estimate of While the growth and risk factors do not correspond its coefficient is negative. exactly to what most capital-market theory tells us is relevant, One question pertaining to the figures presented here stems research with respect to this particular industry lends credence from the interpretation of the significance of the dummy vari- to these variables as defined here (see Malkiel 1970). ables. As it turns out, the class B dummy-variable coefficient Upon regressing the data for the 86 companies included is greater than the class A coefficient, supposedly because of in the sample, all three independent variables are found to a preference for dividend payout, while actually that payout be statistically significant. Of the 86 firms, all of which paid was lower in class B. The question is whether the dummy dividends, 37 firms also had new equity issues. Testing to see that is intended to substantiate the dividend-preference claim whether the 37 firms that issued new equity came from the through the new-issue ratio actually tells us that investors in- same population as those that did not raise new equity, the re- stead attach a higher value to higher earnings retention. The searchers found no essential difference. Since we know there finding of higher P/E ratios resulting from earnings reten- are nontrivial flotation costs associated with the issuance of tion would be consistent with the Litzenberger-Ramaswamy new equity, the finding of no difference between the sub sam- framework cited earlier, and the new-issue effect is somewhat ples implies one of two things: either the costs associated confounded with the dividend effect. with new issues are relatively too small compared to the total From the data we can see that the coefficients did decrease costs of the firm to be detected (despite their large absolute as the new-issue ratios increased, though they were not sig- size, or size relative to the new issue by itself), or a net prefer- nificant, and, not surprisingly, new-issue ratios were rather ence for dividends by holders of electric utility stocks exists highly negatively correlated with dividend payout ratios. that acts to offset the aforementioned expenses. From this we can say, although with some hesitation, that The main thrust of this paper was to assess the impact of external equity appears to be a more costly alternative com- new equity flotation costs on firm value. With the number pared to internal financing when pushed to rather extreme of firms issuing new equity, Van Horne and McDonald were limits. Over more moderate ranges, or those more closely able to calculate new-issue ratios Ð that is, new issues/total aligned with the industry averages, this claim cannot be made shares outstanding at year-end Ð and separate these firms with the same degree of certainty, since we cannot be certain into four groups, leaving those firms issuing new equity in that the payout ratio does not have a positive influence on a separate classification, as indicated in the upper portion of share price, and therefore an inverse relationship to the cost Table 2.2. Adding dummy variables to Equation (2.3), the of equity capital. effect of new issue rates could be analyzed:
P=E D a0 C a1.g/ C a2p C a3.Lev/ C a4.F1/ Default Risk and Dividend Policy (2.4) Ca5.F2/ C a6.F3/ C a7.F4/: where g, compound growth rate; Lev, financial risk measured With the development of the Option Pricing Model, Black and Scholes (1973) have made available a new method of by times interest earned, and F1;F2;F3;F4, dummy vari- ables representing levels of new equity financing. valuing corporate liabilities or claims on the firm. Chen We would expect negative coefficients on the dummy vari- (1978) has reviewed some recent developments in the the- ables if the flotation costs were to be relevant, but in fact all ory of risky debt, and examines in a more systematic fash- coefficients were positive, though only one was significant ion the determinants of the cost of debt capital. Both Reseck (possibly due to small sample size and small relative differ- (1970)andHellwig (1981) have shown that the Modigliani
Table 2.2 New-issue ratios F dummy variable grouping of electric utility firms AB C D E New-issue ratio interval 0 0.001Ð0.05 0.05Ð0.1 0.1Ð0.15 0.15 and up Number of firms in interval 49 16 11 6 4 Mean dividend payout ratio 0:681 0:679 0:678 0:703 0.728 Dummy variable coefficient 1:86 3:23 1:26 0:89 N.A. Dummy variable t-statistic 1:33 2:25 0:84 0:51 (N.A.) From Van Horne and McDonald (1971), Reprinted by permission 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications 27 and Miller (1958 and 1963) arbitrage process that renders their debt obligations at maturity. The tax benefit introduced capital structure irrelevant is generally invalidated if the debt is assumed to be always available to the firm. In instances under consideration is risky and the shareholders enjoy lim- where the interest expense is greater than earnings before ited liability. From this and the 1963 M&M article, we can taxes, the carryback provision of the tax code is used to ob- show that there do exist optimal structures for firms under the tain a refund for the amount of the previously unused tax more realistic conditions mentioned above. shield and, in the event the three-year carryback provision is In the option-pricing framework the two claimants of the not sufficient to make use of the tax shield, Rendleman sug- firm, the debt holders and the equity holders, are easily seen gests that a firm could sell that advantage to another firm by to have conflicting interests; thus one group’s claim can only means of a merger or an acquisition, when the other firm in- be put forth at the expense of the other party. The assumption volved could use the tax benefit. Thus the coupon (net) to be that the total firm value is unchanged is utilized to highlight paid each time period is given by C.1 T/. the wealth-transfer effects, but, as we see in the following At first glance it is apparent that the equity holders gain section, that need not be the case. It is now necessary to find a from this revision, as they are alleged to in the 1963 tax- way to value corporate debt when default risk is introduced. corrected model of M&M. But something else is at work as If the total value of the firm is known or given (this value well: Since the firm is subject to a lower debt-service require- should be reasonably well known or approximated prior to ment, it can build a larger asset base, which serves to act as debt valuation as the former is an upper bound on the latter), insurance in the case of default probabilities owing to the then once the debt value is established the total equity value small net coupon payment. In short, the risk premium asso- falls out as the residual. It is also required that we know how ciated with debt is reduced and the value of the stock, given to perform the transfer of wealth (since the stated goal of in Equation (2.5) can be rewritten as shown below: corporate finance is to maximize the shareholders’ wealth), and learn of any possible consequences that could result from C.1 T/ S D V .1 L /; (2.6) such attempts. r Merton (1974) sought to find the value of risky corporate where all the variables are as defined before and L is less debt, assuming that the term structure of riskless interest than the L given before because of the lessened default risk. rates was flat and known with certainty. This was an indi- It has been argued above that the bondholders benefit rect goal, since the true emphasis lay in finding a way to when interest is tax-deductible, excluding the possibility here value the equity of the firm as a continuous option. The that an overzealous attempt to lever the firm is quickly under- further assumption of consol-type debt was also employed in taken when the tax-deductibility feature is introduced, and an attempt to avoid the transactions-cost arguments involved Equations (2.5)and(2.6) seem to indicate that the value of with rolling over debt at maturity. Invoking Modigliani and the shareholders’ claim also increases, although we have not Miller’s Proposition I (M&M 1958) and allowing for risky yet provided any theoretical justification for such a statement. debt, we find the value of the stock to be the difference be- Rendleman’s analysis gave us the L-value, which is the tween the value of the firm as a whole and the value of the to- clue to this seeming problem. Management can act in a tal debt financing employed to support that whole. Explicitly, way to jeopardize the bondholders’ claims by issuing more debt and thus making all debt more risky, or by undertaking C S D V .1 L/; (2.5) projects that are riskier than the average project undertaken r by the firm. This is the subject of the next section. where S, total value of the firm’s stock; V ,totalfirm Another possibility is to pay large dividends so as to de- value; C , constant coupon payment on the perpetual bonds; plete the firm of its resources, thus paying off the share- r, riskless rate of interest; L, a complicated risk factor asso- holders but hurting the bondholders. Black (1976) goes so ciated with possible default on the required coupon payment. far as to suggest that the firm could liquidate itself, pay out The last term of Equation (2.5) is more often represented the total as a dividend, and leave the bondholders holding by B, the value of the total debt claims outstanding against the proverbial bag. Bond covenants, of course, prevent this the firm, stated in a certainty-equivalent form. It should be sort of action (hence, agency theory), and if a firm could not apparent from this equation that by introducing a greater sell its growth opportunities not yet exploited in the market, probability of default on the debt while maintaining firm this may not maximize the shareholder’s wealth, either, but value, the equity holders gain at the expense of the bond- within bounds it does seem a reasonable possibility. holders. In their review article, Barnea, Haugen, and Senbet (BHS, Rendleman (1978) took Merton’s model and adapted it 1981) discuss the issues related to market imperfections, to allow for the tax deductibility of interest charges. As in agency problems, and the implications for the considera- 2 the Merton article, debt is assumed to be of perpetual type, tion of optimal capital structures. The authors make use consols Ð a justifiable assumption as most firms roll over of M&M’s valuation theory and option-pricing theory to 28 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications reconcile the differences between academicians and prac- We identify a firm Q, which faces several investment titioners about the relevance of financing and dividend opportunities of varying characteristics. The objective is to policies. They arrive at the conclusion that, without fric- identify those projects that are in the stockholders’ interest tionless capital markets, agency problems can give rise to (i.e., they maximize the change in the firm’s market value potential costs. These costs can be minimized through com- ex-dividend at the end of the successive time periods t D plex contractual arrangements between the conflicting par- 0;1;:::;T) and undertake them in order of their relative val- ties. Potential agency costs may help to explain the evolution ues. We specify relative values so that project divisibility re- of certain complexities in capital structure, such as conver- mains possible, as was assumed by Myers. Required is a fi- sion privileges of corporate debt and call provisions. If these nancing plan that specifies the desired mix of earnings re- agency costs are real, then financial contracts that vary in tained, debt outstanding, and proceeds from the issuance of their ability to reduce these costs may very well sell at differ- new equity shares. ent equilibrium prices or yields, even if the financial market- Let dV be a general function of four factors in a direct places are efficient. An optimal capital structure can be ob- sense: (i) the proportion of each project j accepted, xj ; (ii) tained when, for each class of contract, the costs associated the stock of debt outstanding in period t;yt ; (iii) the total with each agency problem are exactly balanced by the yield cash dividends paid in period t, Dt ; and (iv) the net proceeds differentials and tax exposures. Overall, BHS show that opti- from equity issued in period t;Et . For future use let Z be mal capital structures can exist and that this is still consistent denoted as the debt capacity of the firm in period t, this being with the mainstream of classical finance theory. defined as a limit on yt imposed internally by management or by the capital markets, and Ct is the expected net after-tax cash flow to the firm in time period t. The problem can now 2.4 Interactions Between Financing be written as: and Investment Decisions Maximize dV.xj ;yt ;Dt ;Et / D W; Myers (1974) has analyzed in detail the interactions of corporate financing and investment decisions and the im- subject to the constraints; plications therein for capital budgeting. He argues that the existence of these interaction effects may be attributable to .a/Uj D xj 1 0.j D 1;2;:::;J/I the recognition of transaction costs, corporate taxes, or other F market imperfections. Ignored in his analysis is the probabil- .b/Ut D yt Zt 0.t D 1;2;:::;T/I (2.7) ity of default on debt obligations, or, as could otherwise be C .c/U D Ct Œyt yt 1.1C.1 /r/ CDt Et 0; interpreted, changes in this default risk. As alluded to in the t previous section, if we consider possible effects of default where £ and r are the tax rates and borrowing rates, re- risk on the firm’s investment and financing decisions, then spectively. Both are assumed constant for simplicity, but in further analysis must be performed to determine how these actuality both could be defined as functions of other vari- interactions can affect the wealth positions of shareholders ables. Constraints (a) and (b) specify the percentage of the and bondholders. In this section we will analyze this issue project undertaken cannot exceed 100%, and the debt out- by considering both the risk-free debt case and the risky debt standing cannot exceed the debt capacity limit. Constraint (c) case. Chapter 92 and Chap. 60 discuss the theoretical and is the accounting identity, indicating that outflows of funds empirical issues of capital structure. equal inflows, and could be interpreted as the restriction that the firm maintain no excess funds. Constraint (b) can be used to investigate the interaction 2.4.1 Risk-Free Debt Case between the firm’s financing and investment decisions by ex- amining the necessary conditions for optimization. If we as- Following Myers (1974), the basic optimization framework sign the symbols Lj ;Lft,andLct to be the shadow prices is presented in accordance with well-accepted mathemati- on constraints (a)Ð(c), respectively, and let Aj D dW=dxj , cal programming techniques as discussed in the literature of Ft D dW=dyt ;Zjt D dZt =dxj ,andCjt D dCt =dxj , we can capital-rationing. It is presented as a general formulation; it rewrite Equation (2.7) in Lagrangian form as the following: should be considered one approach to analyzing interactions and not the final word per se. Specific results derived by 0 Max W D W Lj .xj 1/ Lft.yt Zt / Chambers et al. (1982), will be used later to demonstrate the L f C Œy y .1 C .1 t/r/ g importance of considering alternative financing mixes when ct t t t 1 evaluating investment opportunities. C.Dt Et /: (2.70) 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications 29
The necessary first-order conditions for the optimum are tax purposes. This procedure will be further investigated in shown as Equations (2.8) through (2.11), with accompany- the following section when we compare it with other well- ing explanations. For each project: accepted capital-budgeting techniques. When dividend policy is not irrelevant, the standard argu- XT ment arises as to whether the preference for dividends, given Aj C Œ Lft Zjt C Lct Cjt Lj 0 (2.8) their general tax status, outweighs the transaction costs in- tD0 curred by the firm when dividends are paid and new financing This can be interpreted as follows: The percentage of a must be raised. In this framework, dividends are viewed as project undertaken should be increased until its incremental another cash flow and, as such, the issue centers on whether cost exceeds the sum of the incremental value of the project, the cash flows from the project plus any increases in the debt the latter consisting of the added debt capacity and the value capacity of the firm are adequate to cover the cost of financ- of the cash flows generated by that project. The incremen- ing, through whatever means. Although we are unable to discern the effect of dividend tal increase in value of the firm obtained by increasing xj to this maximum point is termed the Adjusted Present Value, policy on the value of the firm, it is not outside the solution APV (“adjusted” because of the consideration of interaction technique to incorporate such efforts by including the related effects). expenses as inputs to the numerical-solution procedure. We can examine each of these effects in turn. For the debt It is generally assumed that these interaction effects exist, constraint in each period: so if we are to consider disregarding them, as some would in- sist, we must know what conditions are necessary for lack of dependence of financing and investment decisions. As Myers Ft Lft C Lct Lc;t 1 Œ1 C .1 /r 0: (2.9) points out, only in a world of perfect markets with no taxes is For the constraint implied on dividends: this the case. Otherwise, the tax deductibility of the interest feature of debt suggests that the APV method gives a more dW accurate assessment of project viability than does the stan- Lct 0I (2.10) dard NPV method. dDt and for the new equity constraint:
dW Risky Debt Case C Lct 0: (2.11) dEt Rendleman (1978) not only examined the risk premiums While Equations (2.8)Ð(2.11) are all of interest, the focus is associated with risky debt, but also considered the impact on Equation (2.8), which tells us that the Net Present Value that debt financing could have on equity values, with taxes (NVP) rule commonly put forth should be replaced by the and without. The argument is to some extent based on the APV rule, which accounts for interaction effects. validity (or lack thereof) of the perfect-market assumption Specifically considering the financing constraint, often invoked, which, interestingly enough, turns out to be a Equation (2.9), we would like to be able to find the value double-edged sword. of this constraint, which is most easily done by assuming Without taxes, the original M&M article claims, the in- for the moment that dividend policy is irrelevant. Combined vestment decision of a firm should be made independent of with Equations (2.8)and(2.9) and the definition of APV we the financing decision. But the financing base of the firm 3 obtain ; supports all the firm’s investment projects, not some specific project. From this we infer that the future investments of a XT firm and the risk premiums embodied in the financing costs APVj D Aj C Zjt Ft (2.12) tD0 must be considered when the firm takes on new projects. If, for example, the firm chooses to take on projects of higher- which, in the spirit of the M&M with-tax firm-valuation than-average risk, then this may have an adverse effect on model, tells us that the value of a project is given by the in- the value of the outstanding debt (to the gain of the share- crease in value that would occur in an unlevered firm, plus holders), and the converse holds true as well. It follows that the value of the debt the project is capable of supporting. This the management of a firm should pursue more risky projects follows from the firms ability to deduct interest expenses for to transfer some of the firm’s risk from the shareholders to 30 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications the bondholders, who do not receive commensurate return 2.5 Implications of Financing and Investment for that risk. If the bondholders anticipate this action on Interactions for Capital Budgeting the part of management, then it is all the more imperative that management takes the action because the bondholders This section is intended to briefly review capital-budgeting are requiring and receiving a risk premium, for which they techniques, explain how each in turn neglects accounting are not incurring the “standard” or market-consensus level for financing influences in investment-opportunity analysis, of risk. and discuss the method by which they do incorporate this Myers (1977) presents an argument in which a firm should aspect of financial management into the decision process. We issue no risky debt. The rationale for this strategy is that a will draw heavily on the work of Chambers et al. (1982), in firm possesses certain real options, or investment opportu- making particular distinctions between methods most often nities, that unfold over time. With risky debt some of these covered in corporate-finance textbooks and presumably used investment projects available only to the firm of interest may in practice, presenting numerical comparisons derived from not be undertaken if it is in the interest of the sharehold- varying sets of circumstances. ers to default on a near-term scheduled debt payment. In Chambers, Harris, and Pringle (CHP) examined four stan- this way risky debt induces a suboptimal investment policy dard, discounted cash-flow models and considered the impli- and firm value is not maximized as it would be if the firm cations of using each as opposed to the other three. By way issued no risky debt. One problem here is that we do not of simulation, they were able to deal with differences in fi- have strict equivalence between equity-value maximization nancing projects as well as with possible differences in the and firm-value maximizations, so investment policy cannot risk underlying the operating cash flows generated by each be thought of entirely in terms of firm-value maximization. project. The problem inherent in this and any project evalu- This is a quirk associated with the option-pricing framework ation (not withstanding other difficulties) is in concentrating when applied to firm valuation, and it clouds the determina- on the specification of the amount of debt used to finance tion of what is suboptimal in the finance area.4 the investment project. Project debt is therefore defined as Although we concede that we aren’t entirely sure as to the additional debt capacity afforded the firm as a result of how we should treat the interaction effects of financing and accepting the project, and can alternatively be described as investment policy, we can state with some degree of certainty the difference between the firm’s optimal debt level with the that, even in the absence of the tax deductibility of interest, project and without it. Conceptually this is a fairly concrete these two finance-related decisions are interdependent and, construct, but it still leaves some vague areas when we are as a result, the financial manager should remain wary of actually performing the computations. those who subscribe to the idea that financing decisions do It is essential to arrive at some value estimate of the not matter. estimated cash flows of a project. The CHP analysis consid- Allowing the tax deductibility of interest, it is ironic to ered the following four methods: (i) the Equity Residual note that the conclusions are not nearly as clear-cut as before. method; (ii) the “after-tax Weighted Average Cost-of- If the firm undertakes further, more risky projects, the value Capital” method; (iii) the “Arditti-Levy” weighted cost-of- of debt may actually increase if the firm does not issue fur- capital method; and (iv) the Myers “Adjusted Present Value” ther debt. The shareholders gain from the new project only method. For simplicity, Table 2.3 contains the definitions of on its own merits. If no additional debt financing is raised, the symbols used in the following discussion, after which it is impossible to obtain a larger tax shield and the debt we briefly discuss the formulation of each method, and then may actually become more secure as a result of the larger elaborate on the way in which each method incorporates asset base. If, however, the firm does issue more debt and in interacting effects of financing and investment decisions. that way acts to jeopardize the currently outstanding debt, the number of considerations multiply, and analysis becomes ex- ceedingly difficult because the value of the project by itself, plus the value of the added tax shield, needs to be considered Equity-Residual Method in light of the possible shifting of wealth due to transfers of risk among claimants of the firm. Thus it seems that, when The equity-residual method is formulated in Equation (2.13) we allow the real world to influence the model, as it well in a manner that emphasizes the goal of financial manage- should, the only thing we can say for certain about financing ment, the pursuance of the interests of shareholders: and investment decisions is that each case must be considered separately. 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications 31
Table 2.3 Definitions R D Pretax operating cash revenues of the project during period t; of variables t Ct D Pretax operating cash expenses of the project during period t;
dept D Additional depreciation expense attributable to the project in period t;
£c D Applicable corporate tax rate; I D Initial net cash investment outlay;
Dt D Project debt outstanding during period t; NP D Net proceeds of issuing project debt at time zero;
rt D Interest rate of debt in period t;
ke D Cost of the equity financing of the project;
kw D After-tax weighted-average cost of capital (i.e., debt cost is after-tax);
kAL D Weighted average cost of capital Ð debt cost considered before taxes; ¡ D Required rate-of-return applicable to unlevered cash-flow series, given the risk class of the project
r, ke,and¡ are all assumed to be constant over time
XN Œ. Rt Ct dep rDt /.1 c / C Dt . Dt DtC1 / NPV.ER/ D t ŒI NP : (2.13) .1 C /t tD1 ke
The formula presented above can be interpreted as stating 2.5.1 Arditti and Levy Method that the benefit of the project to the shareholders is the present value of the cash flows not going to pay operating The Arditti-Levy method is most similar to the after-tax expenses or to service or repay debt obligations. weighted-average cost-of-capital method. This formulation With these flows identified as those going to shareholders, can be written as: it is appropriate, and rather easy, to discount these flows at the cost of equity. The only difficulty involved is identifying this cost of equity, a problem embodied in all capital-budgeting NPV.AL/ XN methods. Œ. R C dep rD /.1 / C dep C rD D t t t t c t t I .1 C /t tD1 kAL (2.15) After-Tax, Weighted-Average, Cost-of-Capital It was necessary to restate the after-tax, weighted-average, Method cost-of-capital formula in this manner because the tax pay- ment to the government has an influence on the net cash The after-tax, weighted-average, cost-of-capital method, de- flows, and for that reason the cash-flow figures would be picted in Equation (2.14), has two noticeable differences misleading. To rectify this problem the discount rate must from the formulation of the equity-residual method: now be adjusted as the interest tax shield is reflected in the cash flows and double counting would be involved. XN . Rt Ct dep /.1 c / C dep While the after-tax, weighted-average cost of capital recog- NPV D t t I: t (2.14) nized the cost of debt in the discount rate, it was akin to the .1 C kw / tD1 equity-residual method in considering only returns to equity. First, no flows associated with the debt financing appear in The Arditti and Levy formulas imply that a weighted aver- the numerator, or as relevant cash flows. Second, the cost of age discount rate including the lower cost of debt could only (or best) be used if all flows to all sources of financing were capital is adjusted downward, with kw being a weighted aver- age of debt and equity costs, the debt expense accounted for included; hence the term rDt is found at the end of the first on an after-tax basis. In that way debt financing is reckoned term. This can be rationalized if one considers the case of a firm where there is one owner. The total cash flow to the with in an indirect manner. With the assumption that r and ke owner is the relevant figure, and the discount rate applicable are constant over time, kw can be affected only by the debt- to-equity ratio, a problem most often avoided by assuming a is simply a weighted average of the two individual required fixed debt-to-equity ratio. rates of return. 32 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications
Table 2.4 Application of four Inputs: (1) k D 0:112 (2) r D 0:041 (3) D 0:46 (4) D 0:0802 (5) w D 0:6 capital budgeting techniques e c Method NPV results Discount rates
1. Equity-residual $230:55 ke D 0:112
2. After-tax WACC 270:32 kw D 0:058
3. Arditti-Levy WACC 261:67 kAL D 0:069 4. Myers APV 228:05 r D 0:041 and D 0:0802 From Chambers et al. (1982). Reprinted by permission
2.5.2 Myers Adjusted-Present-Value Method year for all 5 years of the project’s life. Debt financing comprises $600 of the project’s total financing and the prin- This method, derived in Sect. 2.4, is closely related to the cipal is repaid over the five time periods in equal amounts. Arditti-Levy method except for the exclusion of the interest- The discount and tax rates employed are included below in expense flows to the bondholders. In treating the financing Table 2.4 with the results for each of the four methods. mix, Myers implicitly assumes that the tax shield, created by Because the Arditti-Levy method recognizes the acquisi- the interest payments and afforded to the equity holders, has tion of the debt capital and uses a lower discount rate, as does the same risk for the equity holders as the coupon or interest the after-tax WACC, these two methods give the highest net- payments have for the bondholders. Instead of aggregating present-value figures. The equity-residual method recognizes all factors and attempting to arrive at a suitable weighted- only the $400 outflow at time zero, but the higher discount average discount rate, Myers found it less difficult to leave suppresses the net-present-value figure. The Myers APV operating- and financing-related flows separated, and to dis- method, though discounting financing-related flows at the count each at an appropriate rate. This formulation can be cost of debt, also attains a low net-present-value figure be- written as: cause the majority of the flows are discounted at a higher unlevered cost-of-equity rate. XN Basically we can speak of three differences in these meth- . Rt Ct dep /.1 c / C dep APV D t t ods that create the large discrepancies in the bottom-line .1 C /t tD1 figures. The risk factor, reflected in discount rates that may vary over time, is a major element, as was evidenced in the XN rD I C c t : (2.16) example shown above. The pattern of debt and debt payments .1 C r/t tD1 will also be an important factor, particularly so when the debt repayment is not of the annuity form assumed earlier. Fi- This formulation appears to be closely related to the nally, the recognition and valuation of the debt tax shields Modigliani and Miller with-tax firm-valuation model, and will play an important role in net-present-value determina- well it should, given Myers’ motivation for this work. We tion, especially when the constant-debt-repayment assump- choose not to discuss it here, but the reader should be aware tion is dropped and the interest expenses and associated tax that Myers’ emphasis was not solely on the tax advantage of shields grow larger. debt, as the last term in the above equation tends to imply. In the CHP study the valuation models described earlier The four methods are obviously comparable, but usually were employed in a simulation procedure that would allow give different figures for the net present value. The equity- the assessment of the investment proposal. The inputs to the residual, after-tax, weighted-average cost-of-capital and the capital-budgeting procedures were varied across simulations, Arditti-Levy weighted-average, cost-of-capital formulations and the effects of the changes in each input were scrutinized are comparable if the value of the debt outstanding remains a from a sensitivity-analysis viewpoint. They considered, but constant proportion of the remaining cash flows; this is often did not dwell upon, the effects of changing discount rates taken to mean a constant debt ratio. This will not guaran- over time or by some scaling factor on the bottom-line val- tee that the Myers APV method will yield the same results, uation figures; further discussion was deferred primarily be- although the Myers method is equivalent to the other three cause of the multitude of possible combinations that would only if the project life can be described as one period, or as be of interest. Compounding the problem, one would also be infinite with constant perpetual flows in all periods. By way interested in different debt-equity combinations and the ef- of numerical examples we now address the task of determin- fects these would have with changing discount rates, as the ing the factors that create the differences in the net-present- weighting scheme of the appropriate discount rates plays an value figures generated by each method. integral part in the analysis. In avoiding this aspect of the The first example involves the simplest case, where a analysis, the projects evaluated in the forthcoming discus- $1,000 investment generates operating flows of $300 per sion will be viewed as being of equivalent risk, or as coming 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications 33
Table 2.5 Inputs for simulation Project Net cash inflows per year Project life 1 $300 per year 5 years 2 $253.77 per year 5 years 3 $124.95 per year 20 years 4 $200 per year, years 1Ð4 5 years $792.58 in year 5 For each project the initial outlay is $1,000 at time t D 0, with all subsequent outlays being captured in the yearly flows Debt schedule Market value of debt outstanding remains a constant proportion of the project’s market value Equal principal repayments in each year Level debt, total principal repaid at termination of project
Inputs: ke D 0:112 r D 0:041
kw D 0:085 .M &M/ D 0:0986
M D 0:085 c D 0:46 W D 0:3 From Chambers et al. (1982). Reprinted by permission from the same risk class. Lest the reader feel shortchanged, with a larger final payment in year 5, intended to simulate an it is suggested that one examine each method and verify for ongoing project with terminal value in year 5. him or herself what changes would be produced in the net- The results of the simulations are presented in Table 2.6. present-value figures with varying debt schedules. For purposes of comparison, the net-present-value figures of More in tune with the basic theme of this chapter, we the after-tax, weighted-average cost of capital are reported go on to consider the effects that changing financing mixes, first, for two reasons. The after-tax weighted-average cost of debt-payment patterns, and project lives have on the figures capital is probably the best-known technique of capital bud- attained for each of the four methods considered, the first geting, and its net present value figures are insensitive to the (financing mix) being the major issue involved. debt schedule. The initial weights of the debt and equity used In confronting mix effects, we are required to select a to support the project are all that are used in calculating the model for valuing debt in the Myers APV method because weighted discount rate, rendering the repayment pattern of ¡ (the unlevered cost of equity capital) is unobservable. In debt irrelevant. this case we must choose between numerous alternatives, the As indicated earlier, the after-tax weighted-average cost most notable being those of Modigliani and Miller (1963), of capital, Arditti-Levy weighted-average cost of capital, and where debt provides an interest-tax shield, and that of Miller the equity-residual methods are all equivalent if the debt ra- (1977), where the inclusion of personal taxes on investor in- tio is held constant. It is also of interest here that the Myer’s terest income has the effect of perfectly offsetting the tax APV figures, using the Miller method for determining the shield the firm receives, rendering the debt tax advantage cost of capital, are constant over debt schedules; they are, for moot. In the simulation results of CHP presented in the all intents and purposes, the same as the after-tax, weighted- following paragraphs, the Myers cost of unlevered equity average cost-of-capital figures, a finding that is reasonable if capital is computed using each method, with subscripts de- one believes that the cost of debt capital is the same as that of noting the particular method used. unlevered equity. Of all the methods cited above, the equity- Four projects of varied cash-flow patterns and lives are residual method is the most sensitive to the debt schedule em- to be presented and valued, each of which will be simulated ployed, with both principal and interest payments included in with three different debt schedules. Brief descriptions of the the cash flows, a feature compounded by the higher discount projects and debt schedules can be found in Table 2.5, along rates included in the computations. The two methods that in- with the fixed inputs to be used in the actual computations. clude the interest tax shield, the Arditti-Levy method and the The projects’ cash flows, as listed in the table, were actu- Myers APV (M&M) method are also sensitive to the amount ally manipulated in a predetermined way, so that the more in- of debt outstanding, the interest tax shield being of greater teresting cases would be presented. Project 1 is simply a base value the longer the debt is outstanding. In all cases the latter figure, while project 2 has a cash-flow pattern that makes method gives the lowest net-present-value figures due to the the net present value 0, when using the after-tax, weighted- treatment of the interest tax shield. average cost of capital. Project 3 has a longer life, and thus In further simulations CHP showed (and it should be will serve as a method of determining the effects of increas- no surprise) that as higher levels of debt are employed ing project life. Finally, Project 4 has four level payments and higher tax rates are encountered, the magnitude of the 34 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications
Table 2.6 Simulation results Net-present-value under alternative debit schedule
Project Capital budgeting Constant debt ratio Equal principal Level debt 1 After-tax WACC 182 182 182 Arditti-levy WACC 182 179 187 Equity-residual 182 167 202 Myers APV (M&M) 160 157 166 Myers APV (M) 182 182 182 2 After-tax WACC 000 Arditti-Levy WACC 0 17 Equity-Residual 0 332 Myers APV (M&M) 18 19 10 Myers APV (M) 000 3 After-tax WACC 182 182 182 Arditti-Levy WACC 182 169 186 Equity Residual 182 128 194 Myers APV (M&M) 138 119 150 Myers APV (M) 182 182 182 4 After-tax WACC 182 182 182 Arditti-Levy WACC 182 174 182 Equity Residual 182 147 183 Myers APV (M&M) 155 146 156 Myers APV (M) 182 182 182 From Chambers et al. (1982). Reprinted by permission
differences is amplified, and the method employed in the In this book, Chap. 56 discusses the capital structure and capital-budgeting decision takes on greater and greater im- CEO entrenchment in Asia. Moreover, Chap. 60 discusses portance. Even so it was argued that changes associated with the theory and application of alternative methods to deter- changes in the inputs of the longest-lived project, where the mine optimal capital structure. Finally, Chap. 92 provides changes in the net-present-value figures were the most pro- discussion on the capital structure and entry deterrence. nounced, were not that great when compared with the out- comes associated with changing the estimates of the cash flows by as little as 5%. The importance of this finding 2.6 Implications of Different Policies is that projects that are of short duration and are financed on the Beta Coefficient with relatively little debt are not as sensitive to the capital- budgeting technique employed. But, in the case of longer- Investment, financing, dividend, and production policy are lived projects, the method selected can have serious impli- four important policies in financial management decision. In cations for the acceptance or rejection of a project, partic- previous sections, we have discussed investment, financing ularly when higher levels of debt financing are employed. and dividend policies. In this section, we will discuss the Analysts undoubtedly possess their own views as to which impacts of financing, production and the dividend policy on method is stronger conceptually and, in the event of capital- beta coefficient determination. budgeting procedures, should be aware of the debt policy to be pursued. Even in light of these views, it may be prudent to use the Myers APV method with the M&M unlevered-equity cost-determination method as the first screening device for a Impact of Financing Policy on Beta Coefficient project or set of projects. Since this method yields the most Determination conservative figures, any project that appears profitable fol- lowing this analysis should be undertaken, and any project Suppose that the security is a share in the common stock failing this screening can be analyzed using the methods cho- of a corporation. Let us assume that that this corporation sen by the financial manager, if further analysis is thought to increases the proportion of debt in its capital structure, all be warranted. other relevant factors remaining unchanged. How would you 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications 35 expect this change to affect the firm’s beta? We have seen where r, the risk-free rate; RQm, return on the market that an increase in the level of debt leads to an increase in the portfolio; eQ, random price disturbances with zero mean; E D riskiness of stockholders’ future earnings. To compensate for .@P=@Q/.Q=P /, an elasticity constant; b, contribution of this additional risk, stockholders will demand a higher ex- labor to total output; D 1 cov.vQ; RQm/,and ,themarket pected rate of return. Therefore, from Equation (2.17), beta price of systematic risk. must rise for this company’s stock. We see that, all other In addition, the VES production function in two fac- things equal, the higher the proportion of debt in a firm’s tors capital .K/ and labor .L/ can be defined as follows in capital structure, the higher the beta of shares of its com- Equation (2.19). mon stock. Q D K˛.1 s /ŒL C . 1/K ˛s (2.20) B.1 c/ ˇL D ˇU 1 C (2.17) S where Q is firm’s output and ˛; s,and are parameters with the following constraints: where ˇL is the leveraged bet; ˇU is the unlevered operating beta; B is the amount of debt; S is the amount of equity; and ˛>0; c is the corporate tax rate. 0
Arditti, F. D. and H. Levy. 1977. “The weighted average cost of capital Lee, C. F. and A. C. Lee. 2006. Encyclopedia of finance, Springer, as a cutoff rate: a critical analysis of the classical textbook weighted New York average.” Financial Management 6(3), 24Ð34 Lee, C. F., W. Chunchi, and D. Hang. 1993. “Dividend policy under Ang, J. S. and J. H. Chua. 1982. “Mutual funds: different strokes for conditions of capital markets and signaling equilibrium.” Review of different folks.” The Journal of Portfolio Management 8, 43Ð47 Quantitative Finance and Accounting 3, 47Ð59 Barnea, A., R. A. Haugen and L. W. Senbet. 1981. “Market imperfec- Lee, C. F., S. Rahman, and K. Thomas Liaw. 1990. “The impacts of mar- tions, agency problems, and capital structure: a review.” Financial ket power and capital-labor ratio on systematic risk: a Cobb-Douglas Management 10, 7Ð22 approach.” Journal of Economics and Business 42(3), 237Ð241 Baron, D. P. 1975. “Firm valuation, corporate taxes, and default risk.” Journal of Finance 30, 1251Ð1264 Lee, C. F., K. C. Chen, and K. Thomas Liaw. 1995. “Systematic risk, Baumol, W. and B. G. Malkiel. 1967. “The firm’s optimum debt- wage rates, and factor substitution.” Journal of Economics and Busi- equity combination and the cost of capital.” Quarterly Journal of ness 47(3), 267Ð279 Economics 81(4), 546Ð578 Levy, H. and M. Sarnat. 1972. Investment and portfolio analysis, Wiley, Black, F. 1976. “The dividend puzzle.” Journal of Portfolio Manage- New York ment, 5Ð8 Litzenberger, R. H. and K. Ramaswamy. 1979. “The effect of personal Black, F. and M. Scholes. 1973. “The pricing of options and corporate taxes and dividends on capital-asset prices: theory and empirical ev- liabilities.” Journal of Political Economy 81(3) 637Ð654 idence.” Journal of Financial Economics 7, 163Ð195 Chambers, D. R., R. S. Harris, and J. J. Pringle. 1982. “Treatment of fi- Litzenberger, R. H., and H. B. Sosin. 1979. “A comparison of capital- nancing mix in analyzing investment opportunities.” Financial Man- structure decision of regulated and nonregulated firms.” Financial agement 11, 24Ð41 Management 8, 17Ð21 Chen, A. H. 1978. “Recent development in cost of debt capital.” Journal of Finance 33, 863Ð877 Malkiel, B. G. 1970. “The valuation of public-utility equity.” Bell Jour- Conine, T. E. Jr. 1980. “Debt capacity and the capital budgeting deci- nal of Economics and Management Science 1, 143Ð160 sion: a comment.” Financial Management, 20Ð22 Martin, J. D. and D. F. Scott. 1976. “Debt capacity and the capital bud- DeAngelo, H. and L. DeAngelo. 2006. “The irrelevance of the MM geting decision.” Financial Management 5(2), 7Ð14 dividend irrelevance theorem.” Journal of Financial Economics 79, Martin, J. D. and D. F. Scott Jr. 1980. “Debt capacity and the capi- 293Ð315 tal budgeting decision: a revisitation.” Financial Management 9(1), Fama, E. F. and M. H. Miller. 1972. The theory of finance, Holt, 23Ð26 Rinehart and Winston, New York Merton, R. C. 1974. “On pricing of corporate debt: the risk structure of Gahlon, J. M. and R. D. Stover. 1979. “Debt capacity and the capital interest rates.” Journal of Finance 29, 449Ð470 budgeting decision: a caveat.” Financial Management 8, 55Ð59 Miller, M. H. 1977. “Debt and taxes.” Journal of Finance 32, 261Ð275 Gupta, M. C. and A. C. Lee. 2006. “An integrated model of debt is- suance, refunding, and maturity.” Review of Quantitative Finance Modigliani, F. and M. H. Miller. 1958. “The cost of capital, corpo- and Accounting 26(2), 177Ð199 rate finance, and theory of investment.” American Economic Review Gupta, M. C., A. C. Lee, and C. F. Lee. 2007. Effectiveness of dividend 48(3), 261Ð297 policy under the capital asset pricing model: a dynamic analysis. Modigliani, F. and M. H. Miller. 1963. “Corporate income taxes and Working Paper, Rutgers University the cost of capital: a correction.” American Economic Review 53(3), Hamada, R. S. 1972. “The effect of the firm’s capital structure on 433Ð443 the systematic risk of common stocks.” Journal of Finance 27(2), Myers, S. C. 1974. “Interaction of corporate financing and investment 435Ð452 decision.” Journal of Finance 29, 1Ð25 Hanoch, G. and H. Levy. 1969. “The efficiency analysis of choices in- Myers, S. C. 1977. “Determinants of corporate borrowing.” Journal of volving risk.” Review of Economic Studies 36, 335Ð346 Financial Economics 5, 147Ð175 Hellwig, M. F. 1981. “Bankruptcy, limited liability, and the Modigliani- Miller theorem.” The American Economic Review 71, 155Ð170 Porter, R. B. and J. E. Gaumwitz. 1972. “Stochastic dominance Higgins, R. C. 1977. “How much growth can a firm afford?” Financial vs. mean-variance portfolio analysis: an empirical evaluation.” Management 6(3), 7Ð16 American Economic Review 57, 438Ð446 Higgins, R. C. 1981. “Sustainable growth under inflation.” Financial Rendleman, R. J. Jr. 1978. “The effects of default risk on firm’s invest- Management, 36Ð40 ment and financing decisions.” Financial Management 7(1), 45Ð53 Hong, H. and A. Rappaport. 1978. “Debt capacity and the capital- Reseck, R. W. 1970. “Multidimensional risk and the Modigliani-Miller budgeting decision: a caveat.” Financial Management, 7Ð11 hypothesis.” Journal of Finance 25, 47Ð51 Jean, W. 1975. “Comparison of moment and stochastic-dominance Rhee, S. G. and F. L. McCarthy. 1982. “Corporate debt capacity and ranking methods.” Journal of Financial and Quantitative Analysis capital-budgeting analysis.” Financial Management 11, 42Ð50 10, 151Ð162 Rubinstein, M. E. 1973. “A mean-variance synthesis of corporate finan- Jensen, M. and W. Meckling. 1976. “Theory of the firm: managerial cial theory.” Journal of Finance 28, 167Ð187 behavior, agency costs, and ownership structure.” Journal of Finan- cial Economics 3, 305Ð360 Stiglitz, J. 1972. “Some aspects of pure theory of corporate finance: Johnson, D. J. 1981. “The behavior of financial structure and sustain- Bankruptcies and take-overs.” Bell Journal of Economics and Man- able growth in an inflationary environment.” Financial Management agement Science 3, 458Ð482 10, 30Ð35 Tuttle, L., and R. H. Litzenberger. 1968. “Leverage, diversification, and Kim, E. H. 1978. “A mean-variance theory of optimal capital structure capital-market effects on a risk-adjusted capital-budgeting frame- and corporate debt capacity.” Journal of Finance 33, 45Ð64 work.” Journal of Finance 23, 427Ð443 Kim, E. H. 1982. “Miller’s equilibrium, shareholder leverage clienteles, Van Horne, J. C. and J. D. McDonald. 1971. “Dividend policy and new and optimal capital structure.” Journal of Finance 37, 301Ð319 equity financing.” Journal of Finance 26, 507Ð519 Kim, E. H., J. J. McConnell, and P. R. Greenwood. 1977. “Capital- structure rearrangements and me-first roles in an efficient capital market.” Journal of Finance 32, 811Ð821 38 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications
Appendix 2A Stochastic Dominance EF U.X/ > EG U.X/ (2A.1) and its Applications to Capital-Structure Analysis with Default Risk where EF U.X/ and EG U.X/ are expected utilities. Mathe- matically, they can be defined as:
2A.1 Introduction Zx EF U.X/ D U.X/f.X/dx (2A.2a) Mean-variance approaches were extensively used in the x literature to derive alternative finance theories and per- Zx form related empirical studies. Besides mean-variance E U.X/ D U.X/g.X/dx (2A.2b) approaches, there is a more general approach, stochastic- F dominance analysis, which can be used to choose a portfo- x lio, to evaluate mutual-fund performance, and to analyze the where U.X/ D the utility function, X D the investment optimal capital-structure problem. dollar-return variable, f.X/ and g.X/ are probability dis- Levy and Sarnat (1972), Porter and Gaumwitz (1972), tributions of X. It should be noted that the above-mentioned Jean (1975), and Ang and Chua (1982) have discussed first-order stochastic dominance does not depend upon the the stochastic-dominance approach to portfolio choice and shape of the utility function with positive marginal utility. mutual-fund performance evaluation in detail. Baron (1975), Hence, the investor can either be risk-seeking, risk neutral, Arditti and Peles (1977), and Arditti (1980)haveusedthe or risk-averse. If the risk-aversion criterion is imposed, the theory of stochastic dominance to investigate the optimal utility function is either strictly concave or nondecreasing. capital-structure question. In this appendix we will discuss If utility functions are nondecreasing and strictly concave, only how stochastic-dominance theory can be used to ana- then the second-order stochastic-dominance theorem can be lyze the issue of optimal capital structure with default risk. defined. Mathematically, the second-order dominance can be defined as:
2A.2 Concepts and Theorems of Stochastic Zx Dominance ŒG.T / F.t/ dt > 0; where G.t/ ¤ F.t/for some t: x (2A.3) The expected utility rule can be used to introduce the Equation (2A.3) specifies a necessary and sufficient condi- economics of choice under uncertainty. However, this deci- tion for an asset F to be preferred over a second asset G by sion rule has been based upon the principle of utility max- all risk-averters. imization, where either the investor’s utility function is as- Conceptually, Equation (2A.3) means that in order for as- sumed to be a second-degree polynomial with a positive first set F to dominate asset G for all risk-aversion investors, derivative and a negative second derivative, or the probability the accumulated area under the cumulative-probability function is assumed to be normal. A stochastic-dominance distribution G must be greater than the accumulated area theory is an alternative approach of preference orderings for F for any given level of wealth. This implies that, un- that does not rely upon these restrictive assumptions. The like first-order stochastic dominance, the cumulative density stochastic-dominance technique assumes only that individ- functions can cross. uals prefer more wealth to less. Stochastic dominance is an extremely important and pow- An asset is said to be stochastically dominant over erful tool. It is properly founded on the basis of expected utility another if an individual receives greater wealth from it in maximization, and even moreimportant, itappliesto anyprob- every (ordered) state of nature. This definition is known ability distribution. This is because it takes into account every as first-order stochastic dominance. Mathematically, it can point in the probability distribution. Furthermore, we can be be described by the relationship between two cumulative- sure that, if an asset demonstrates second-order stochastic probability distributions. If X symbolizes the investment dol- dominance, it will be preferred by all risk-aversion investors, lar return variable and F.X/ and G.X/ are two cumulative- regardless of the specific shape of their utility functions. probability distributions, then F.X/ will be preferred to Assume that the density functions of earnings per share G.X/ by every person who is a utility maximizer and whose (EPS) for both firm A and firm B are f.X/ and g.X/,re- utility is an increasing function of wealth if F.X/ G.X/ spectively. Both f.X/ and g.X/ have normal distributions for all possible X,andF.X/ < G.X/for some X. and the shape of these two distributions are described in For the family of all monotonically nondecreasing util- Fig. 2A.1. Obviously the EPS of firm A will dominate the ity functions, Levy and Sarnat (1972) show that first-order EPS of firm B if an investor is risk-averse because they both stochastic dominance implies that: 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications 39
Fig. 2A.1 Probability distributions of asset F and asset G
offer the same expected level of wealth .f D g/ and be- earnings X, before taxes and financial charges, such that, in cause the variance of g.X/ is larger than that of f.X/. any state of nature that occurs, both firms have the same earn- Based on both the first-order and the second-order ings. In addition, it is assumed that this random variable X stochastic-dominance theorems mentioned earlier, a new the- is associated with a cumulative-distribution function F.X/. orem needed for investigating capital structure with default Firm A is assumed to be financed solely by equity, while firm risk can be defined as: B is financed by both debt and equity. The market value V1 of firm A equals E1, the value of its equity, while the market Theorem 2A.1. Let F , G be two distributions with mean value V2 of firm B equals the market value of its equity .E2/ values 1 and 2 respectively, such that, for some X0 < 1, plus the value of its debt .D2/. Debt is assumed to sell at its F G for X X0 (and F The cumulative distribution associated with Equation a firm should issue. However, these results have indicated the (2A.7)is: possibility of interior (noncorner) optimal capital structure. By using a linear utility function, Arditti and Peles (1977) ( F.0/ if Y D0; show that there are probability distributions for which an in- G2.Y /D FŒY=˛.1 k/.1 T/ if 0 where ˛.D2 CrD2/ is the critical income level of bankruptcy. Equations (2A.8)and(2A.9) imply that the levered firm 2A.4 Summary cannot dominate the unlevered firm on a first-degree or second-degree stochastic-dominance basis. From the theo- In this appendix we have tried to show the basic concepts un- rem of stochastic dominance that we presented in the previ- derlying stochastic dominance and its application to capital- ous section, it can be concluded that the unlevered firm can- structure analysis with default risk. By combining utility not dominate the levered firm because the expected return of maximization theory with cumulative-density functions, we the levered firm is generally higher than that of the unlevered are able to set up a decision rule without explicitly relying firm (otherwise why levered?), and because the G2.Y / and on individual statistical moments. This stochastic-dominance G1.Y / curves intersect only once. theory can then be applied to problems such as capital- Consequently, a general statement using stochastic domi- structure analysis with risky debt, as was shown earlier. nance cannot be made with respect to the amount of debt that